The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^2+X+2 X^2  1  1 X^2  1  1  1  1  1  1 X^2+2 X^2+X  1  1  1 X+2  1  1  1 X^2  1  1  2  1  1 X^2+X+2  1  1 X+2 X^2  0  1  1  1  1  0  1  1  1  1 X^2  1  1  1  1  1 X^2+X+2  1  1  0 X^2+2  1 X^2+2 X^2+X+2  1  1  1  1  1  X  1  X  1  1  1  1  1 X+2  1  1  1  1
 0  1  1 X^2 X+1  1  X  3  1 X^2+X X+3  1  1  1 X^2 X^2+1  1  2 X^2+3 X^2+X+1  X X^2+X+2 X^2+X+3  1  1  3  X X^2+1  1 X+2 X+2 X+1  1 X^2+X+1 X^2  1  1 X^2+2  1 X^2+1 X^2  1  1  1 X+1 X^2+X+1  2 X+2  1  2 X^2+X X^2+X  2  X X+1 X^2+3  X X^2+2 X^2+X+2  1  0 X^2+X  0  1  0  1  1 X^2+X X^2+X+2  1 X^2 X^2+X+3  1  3 X^2+X+2 X^2+X+3  3  0 X^2+3 X^2+2  1 X+3 X^2 X^2+X+3  0
 0  0  X X+2  2 X+2 X+2  2  0  0  X X^2+X X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X^2+X+2 X^2+2  2  0  0 X^2+X+2 X^2+X+2 X^2+2  2 X^2+X  X X^2 X^2+2 X+2  X  0 X^2  0 X^2+X+2 X^2+2  X  X X+2 X^2+2 X^2+X+2 X^2+X  X X+2 X+2 X^2 X+2 X^2  2  0 X^2+X X^2 X+2  X  X X^2+X  2  X  2 X^2+2  0 X^2 X^2+X+2 X^2+X+2 X^2+X  X  X X+2  2  0 X^2+X  2  0  X X+2  0

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+70x^81+274x^82+362x^83+335x^84+242x^85+198x^86+184x^87+151x^88+92x^89+74x^90+34x^91+16x^92+8x^93+4x^94+1x^98+1x^112+1x^118

The gray image is a code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.484 seconds.